Codex @codex  0

By André Jürgen Massing.

Online text: www.math.ntnu.no/emner/TMA4130/2021h/lectures/ErrorAnalysisNuMeODE.pdf

Authored notes credited to André Massing, identified as André Jürgen Massing by the NTNU profile. Dated 3 October 2021, in the TMA4125/4130/4135 Mathematics 4N/D materials; the university is the host, rather than the author.

Cited passages: André Massing, Numerical solution of ordinary differential equations: One step methods, October 3, 2021, page 1, Example 1.1: Euler and Heun increment functions.

By Rodolfo Ruben Rosales.

Online text: math.mit.edu/classes/18.305/Notes/n00Branch_Points_B_Cuts.pdf

Standalone teaching notes credited to Rodolfo R. Rosales, identified as Rodolfo Ruben Rosales by the MIT profile. The title page says MIT 18.04 and is dated 11 October 1999; the hosting folder 18.305 does not identify its course or authorship of an entire course.

Cited passages: Rosales, Branch Points and Branch Cuts, section 1 and Example 2.4; Rosales, Branch Points and Branch Cuts, section 1, printed pp. 3–8, and Example 2.4, printed p. 15; Rosales, section 1, Definition 1.1 and its clarifications; Rosales, section 1, equation 1.3, and Example 2.4.

By Steven G. Krantz.

Online text: www.math.wustl.edu/~sk/books/guide.pdf

Author-hosted whole manuscript credited to Steven G. Krantz. The inspected title page is dated 14 October 2007; no first-publication or copyright year inferred. Citations use printed chapter pages, rather than the preliminary table-of-contents pagination.

Cited passages: Krantz, A Guide to Complex Variables, sections 9.3.4–9.3.5, printed pp. 158–159; Section 9.3.6, printed p. 159: globally defined holomorphic function; Sections 9.3.1–9.3.3, printed pp. 157–158: terminal elements and fixed endpoint homotopy.

By Arthur Pentland Dempster, Nan M. Laird, Donald B. Rubin.

Published in Journal of the Royal Statistical Society. Series B (Methodological), volume 39, number 1.

Online text: web.mit.edu/6.435/www/Dempster77.pdf

Joint article by Arthur Pentland Dempster, Nan M. Laird and Donald B. Rubin, printed with the byline A. P. Dempster, N. M. Laird and D. B. Rubin. Published in 1977 in Journal of the Royal Statistical Society, Series B, volume 39, number 1. The December 1976 presentation and later scan date are distinct from publication.

Cited passages: Section 1, printed pp. 1 and 3: naming of the two steps and earlier special cases; Section 2, printed p. 6, equation (2.17) and the general E-step/M-step definition; Section 2, printed p. 6: general maximization step; Section 3, printed pp. 6-7, Lemma 1 and Theorem 1, especially equation (3.10); Section 4.3, printed pp. 15-16, especially the paragraph following equation (4.3.3): conditional indicator probabilities and weighted counts.

By John K. Hunter.

Online text: math.ucdavis.edu/~hunter/notes/asy.pdf

The title page credits John K. Hunter and is dated February 2004; copyright 2004 is stated separately. The university is his affiliation and the notes host, rather than an author. No first-publication or online revision date inferred.

Cited passages: §1.1.2, p. 2: regular and singular perturbations; §4.3.5, p. 58: uniform solution and overlap subtraction; §§4.3.3–4.3.4, pp. 57–58: inner expansion and matching.

By Keith Conrad.

Online text: kconrad.math.uconn.edu/blurbs/gradnumthy/rationalsinQp.pdf

Standalone authored expository note. The inspected copy is undated; no publication date is inferred from the search engine or hosting path. It explicitly writes p-adic expansions with low-order terms first.

Cited passages: §1, printed p. 1: p-adic rational expansions and explicit low-order-first convention; §3, Theorem 3.1, printed pp. 3–5: eventual periodicity.

By Jan-Hendrik Evertse.

Online text: kconrad.math.uconn.edu/math5020f11/evertsepadicnotes.pdf

Authored notes dated March 2011. Their running header identifies Master Course Diophantine Equations, Spring 2011. The supplied UConn mirror is hosted within a different Fall 2011 course by Keith Conrad; hosting and teaching that course do not confer authorship of these notes. No publisher or original publication date is inferred.

Cited passages: §3, Theorem 3.4 and digit/congruence discussion, printed pp. 7–9: unique expansion and agreement of low-order digits; §3, printed pp. 6–7: definition of Zp, rational denominators and units.

By Robbert Fokkink.

Published in Nieuw Archief voor Wiskunde, series 5, volume 17, number 4, pp. 275–280.

Online text: www.nieuwarchief.nl/serie5/pdf/naw5-2016-17-4-275.pdf

Cited passages: Robbert Fokkink, Wie weet wie Willem Wijthoff was?, Nieuw Archief voor Wiskunde 5/17(4), December 2016, printed p. 279, Wythoffs bewijs van de stelling van Mantel: attribution of problem 28 in 1907.

By Igor Pak.

Online text: arxiv.org/pdf/1408.5711

Standalone historical preprint, arXiv:1408.5711. Version 1 was submitted on 25 August 2014; the inspected version 2 is dated 27 August 2014. Its cover says the account will appear as an appendix in a forthcoming book by Richard P. Stanley; the authorship here applies to this preprint, not to the whole book.

Cited passages: §§2–3 and §5, printed pp. 2–4: Euler correspondence, Segner recurrence and Catalan's bracketed products.

By Richard P. Stanley.

Online text: math.mit.edu/~rstan/bij.pdf

Authored problem collection. The inspected cover is dated 18 August 2009; this identifies the supplied version rather than a book publication date. The Catalan interpretations occur in §5, printed pp. 38–39, Problems 153–159.

Cited passages: §5, Problem 154, printed p. 38: binary parenthesizations of n+1 letters; §5, printed pp. 38–39, formula (7) and Problems 154–159: Catalan counts, binary parenthesizations, binary trees and Dyck paths.

By Charles M. Grinstead and J. Laurie Snell.

Publisher of the underlying book: American Mathematical Society.

Online text: math.dartmouth.edu/~prob/prob/prob.pdf

The linked CHANCE Project version is dated 4 July 2006. Its cover identifies the underlying second-edition book as copyright 2003 by the two authors, and this version as copyright 2006 by Peter G. Doyle. The version credit does not identify Doyle as an original-book coauthor or formal editor. These dates describe copyrights and a version, rather than a claim about first publication.

Cited passages: §3.1, Example 3.3 and Table 3.1, printed pp. 77–78: uniform-calendar assumptions, distinct-label product and threshold.

Section 6.1, Definition 6.1, printed p. 226, defines finite discrete expectation by summing values weighted by their probabilities. This is the discrete calculation used in nonnegative random variable. Online text: math.dartmouth.edu/~prob/prob/prob.pdf .

By Refael Hassin, Nimrod Megiddo.

Publisher: Elsevier Science Publishing Co., Inc.

Published in Linear Algebra and Its Applications 114/115, 589–602.

Online text: theory.stanford.edu/~megiddo/pdf/orientat.pdf

Cited passages: Hassin and Megiddo (1989), Theorem 2.6 proof, printed p. 592: cycle orientation and contraction, explicitly described as a different constructive proof from Robbins's; Hassin and Megiddo, On Orientations and Shortest Paths (1989), printed pp. 591–592: bridge-connectedness, strong connectivity and Theorem 2.6 (Robbins).

Original work by Euclid. The linked English adaptation and guide are by David E. Joyce, drawing on Thomas Little Heath and other translations. About the Text describes this adaptation; it is not unmodified Heath.

By Keith Conrad.

Online text: kconrad.math.uconn.edu/blurbs/ugradnumthy/perfect-numbers-mersenne.pdf

Cited passages: Theorem 1.1, pp. 1–2: even-number equivalence and proof; §1, Theorem 1.1 and Example 1.2, pp. 1–2.

By Godfrey Harold Hardy, John Edensor Littlewood, George Pólya.

Publisher: Cambridge University Press.

Online text: djvu.online/file/CjwWRpwExRE7j

Cited passages: Inequalities, second edition, §9.8(ii), truncation and integration by parts, printed pp. 242–243; Inequalities, second edition, §9.8, Theorem 327, equation (9.8.2), printed p. 240; Inequalities, second edition, §9.8, Theorem 327, printed p. 240, and sharpness argument on printed p. 243.

First published in 1934; second edition published in 1952.

By Claude Berge.

Publisher: National Academy of Sciences.

Publication information: pubmed.ncbi.nlm.nih.gov/16590096/

Published in Proceedings of the National Academy of Sciences of the United States of America.

Online text: acm.math.spbu.ru/~sk1/download/books/roma/Other/pnas00700-0060.pdf

Cited passages: Claude Berge, Two theorems in graph theory, printed p. 842: finite unoriented graph and Problem 3; printed p. 843, Theorem 1: maximum matching and absence of an alternating chain between neutral points.

Proceedings of the National Academy of Sciences 43(9), pp. 842–844; published 15 September 1957. The paper was communicated on 8 July 1957.

By Leonhard Euler; English translation by Jordan Bell.

Presented to the St Petersburg Academy on 5 December 1735. Published as "De summis serierum reciprocarum" in Commentarii academiae scientiarum Petropolitanae 7 (1740), pp. 123–134. The linked translation is arXiv version 2, dated 5 February 2008.

Online text: arxiv.org/pdf/math/0506415

Cited passages: English translation, p. 1, §2 and publication note; pp. 3–4, §§3–8: sine series, roots and coefficients.

By Jean Gallier.

Online text: www.cis.upenn.edu/~jean/geomcs-v2.pdf

Author-hosted version dated 9 October 2025. This version date is distinct from first publication.

Cited passages: §2.4, Lemma 2.4.1, pp. 23–24; §2.7, Definition 2.7.1, p. 37; §2.7, Definition 2.7.1 and linear-map construction, pp. 37–38.

By Francis Galton.

Published in Journal of the Anthropological Institute of Great Britain and Ireland, volume 15, pp. 246-263.

Online text: galton.org/essays/1880-1889/galton-1886-jaigi-regression-stature.pdf

Cited passages: Printed p. 252: shoes-on versus shoes-off uncertainty and the average two-thirds height-deviation claim; Printed pp. 247-248, Table I; pp. 261-262, explanation of Plate IX(a): adjusted heights, counts, grouped medians and 2:3 deviation ratio.

By Terence Tao.

Course context: 246B, complex analysis. These notes were posted on 23 December 2020.

Publisher: Terence Tao, What's new (author website).

Online text: terrytao.wordpress.com/2020/12/23/246b-notes-1-zeroes-poles-and-factorisation-of-meromorphic-functions/

Cited passages: §1, Theorem 2 and equation (6): neighbourhood of the closed disk, zeros counted with multiplicity, holomorphic special case.